Severn,
Thanks for recommending the New River Trail. I've long wanted to bike it (as well as several others in the Eastern/Mid-Atlantic states) but not yet gotten to it. (Living in California means that those locations are hardly over-nighters.)
Besides the Virginia State Parks website to which you provide a link, there's also an excellent website at <trailink.com>. The right of way was donated to the state by Norfolk Southern but I'm not sure which of its predecessors actually operated the line.
My wife and I do all our riding on regular road bikes with "combination" or "cross-over" tires that have a road or touring surface in the center for easy rolling but more-or-less all-terrain surfaces along the sides which really help on less-developed (or less-maintained) trails.
Bill